Electromagnetic characteristics of A≤3 physical and lattice nuclei

Abstract

We analyze the quark-mass dependence of electromagnetic properties of two- and three-nucleon states. To that end, we apply the pionless effective field theory (EFT) to experimental data and numerical lattice calculations which simulate QCD at pion masses of 450 and 806 MeV. At the physical pion mass, we postdict the magnetic moment of helium-3, ${\ensuremath{\mu}}_{\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{He}}=\ensuremath{-}2.13$ nNM (natural nuclear magneton), and the magnetic polarizability of deuterium, ${\ensuremath{\beta}}_{\text{D}}=7.{3310}^{\ensuremath{-}2} {\mathrm{fm}}^{3}$. Magnetic polarizabilities of helium-3, ${\ensuremath{\beta}}_{\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{He}}=9.{710}^{\ensuremath{-}4} {\mathrm{fm}}^{3}$, and the triton, ${\ensuremath{\beta}}_{\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{H}}=8.{210}^{\ensuremath{-}4} {\mathrm{fm}}^{3}$, are predictions. Postdictions of the effective theory for the magnetic moments are found consistent with QCD simulations at 806 MeV pion mass, while our EFT result ${\ensuremath{\beta}}_{\text{D}}=2.{9210}^{\ensuremath{-}2} {\mathrm{fm}}^{3}$ was not extracted from the lattice. The deuteron would thus be relatively pliable compared to a three-nucleon state for which we postdict ${\ensuremath{\beta}}_{\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{H}}=3.{910}^{\ensuremath{-}5} {\mathrm{fm}}^{3}$. At ${m}_{\ensuremath{\pi}}=450\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, the magnetic moment of the triton is predicted, ${\ensuremath{\mu}}_{\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{He}}=\ensuremath{-}2.15(5)$ nNM, based on a conjecture of its binding energy, ${B}_{\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{H}}\ensuremath{\cong}30$ MeV. For all three pion masses, we compare the point-charge radii of the two- and three-nucleon bound states. The sensitivity of the electromagnetic properties to the Coulomb interaction between protons is studied in anticipation of lattice calculations with dynamical QED.